Screening effect on the binding energy of the exciton in quantum wires

Abstract

This paper describes using the finite difference method to study the screening effect on the binding energy of excitons in quantum wires (QWRs). We have derived an analytical formula for the effective screened interaction potential between an electron and a hole in an exciton. The exciton binding energy as functions of the screening length, carrier density, and QWR width is calculated and is found to be sensitive to the screen length when the length is less than 1 × 103 Å. Furthermore, when the screen length is less than 3 × 102 Å, the exciton binding energy decreases rapidly with decreasing screen length. It is also found that the wider the QWR is, the more pronounced the screening effect will be. The transition from a dilute exciton gas to a dense electron-hole plasma in a QWR is clearly shown on a phase diagram for the carrier density-temperature plane.